Let u $=$ u$1$ u$2$ u$3,$ v $=$ v$1$ v$2$ v$3$ and w $=$ w$1$ w$2$ w$3$ be three vectors in R $3.$ Prove that span$\{$u$,$ v$,$ w$\}=$ R $3$ if and only if det $$ u$1$ v$1$ w$1$ u$2$ v$2$ w$2$ u$3$ v$3$ w$3=0$